2013-07-18

Real Historians Do Bayes!

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by Neil Godfrey

How do historians, comparative linguists, biblical and textual critics, and evolutionary biologists establish beliefs about the past? How do they know the past?

dr_tucker
Aviezer Tucker

That’s the subject of Aviezer Tucker‘s Our Knowledge of the Past: A Philosophy of Historiography (2004). Tucker’s interest is the relationship between the writing of history (historiography) and evidence (p. 8). It is written for audiences interested in philosophy, history, biblical criticism, the classics, comparative linguistics and evolutionary biology (p. 22).

When I began to review Richard Carrier’s book, Proving History, I pointed out that far from substituting crude mathematics for historical inquiry, the application of Bayes’ Theorem merely expresses in symbolic terms the way historians evaluate the nature of evidence and test hypotheses to explain evidence for certain events and artefacts. Some fearful critics have objected to the application of Bayes because they have never understood this fact.

All Bayes’ theorem does is help us clarify our thinking. Bayes theorem is simply a symbolic way of expressing how we do our best thinking when seeking explanations for evidence or evaluating hypotheses against the evidence. The more complex the factors that need to be considered in addressing a problem the easier it is for us to overlook a critical point or draw invalid comparisons. Bayes’ helps us to clarify thinking about the most complex of issues, including those in the social sciences and history. *

Why Bayes?

Tucker writes as a philosopher and concurs with the above assessments of other authors addressed in my earlier posts. Philosophers like to clarify the complexities they are discussing and are apt to use illustrative symbols to this end.

Philosophers find often that formal representation, Bayesian probability in our case, clarifies and concentrates the discussion. Some historians and many classicists may not be as used to this form of representation as their philosophical colleagues. . . . When I use formal representation, I express the same concepts in words, for the benefit of readers who are not accustomed to formal notation. (p. 22)

Historians ask questions like the following:

To what degree does a piece of evidence contribute or not to the confirmation of a hypothesis, given background conditions? (p. 96)

Specifically:

To what extent does a similar saying in the Gospels of Matthew and Luke support, or not support, the Q hypothesis, given everything else we know that is relevant to the question?

To what extent does the passage “born of a woman” in Galatians 4:4 support, or not, the hypothesis that the author believed Jesus was an historical person in the recent past, given everything else we know about Galatians, that verse in particular and its context, and evidence for Jesus?

The Bayesian theorem purports to state formally the relation between a particular piece of evidence and the hypothesis. (p. 96)

In the fifty or so pages of chapter 3 Tucker demonstrates

that an interpretation of Bayesian logic is the best explanation for the actual practices of historians. (p. 96)

The Theorem

Tucker sets out Bayes’ Theorem thus:

Pr(H|E & B) = [Pr(E|H & B) x Pr(H|B)]:Pr(E|B)

Pr — the Probability of. . .

H — the Hypothesis, or any historical proposition about past events

E — the Evidence (often this means similarities between two or more independent sources)

B — the Background knowledge of theories, methods, other hypotheses

The vertical line | should be read as “given”. So the first part of the equation expresses:

The Probability of the Hypothesis being true given the evidence and background information.

Pr(H|E & B) translated into words:

The probability of the hypothesis that George Washington was the first president of the United States, given the massive amount of documentary evidence for it and background knowledge of the causal chains that led to this evidence, is almost 1. We are almost certain that George Washington was the first president. (p. 97)

Contrast this:

The probability of the hypothesis that Jesus was the founder of what became the Christian Church, given the massive documentary evidence for it and background knowledge of the causal chains that led to this evidence, is . . . ?

Unfortunately we have no background knowledge of the causal chains that led to the Gospels and writings of Paul. We only have other hypotheses (e.g. oral tradition) to fill in these gaps.

Pr(H|B) in words:

This is the prior probability of a particular hypothesis being true given our background knowledge prior to knowledge of the evidence.

Thus,

The probability of the hypothesis that there was a city of Troy that was destroyed in a war in the twelfth century BCE was low given the background information that had been known prior to the archaeological discovery of the city.

Compare:

The probability of the hypothesis that there was a Gospel of Thomas that was the text of an “unorthodox” Christian group in the second and third centuries CE was relatively high given the background information that had been known prior to its discovery in 1945 (e.g. Hippolytus of Rome (c. 222–235) and Origen of Alexandria (c. 233) wrote about it.)

Pr(E|H & B) in words:

This “expresses the likelihood of the evidence given the hypothesis in question in conjunction with background knowledge.”

So,

Given the hypothesis that George Washington was the first president of the United States, and background theories and information about the nature of paper and its preservation and use over two centuries and our knowledge of paper trails that governments and politicians generate, it is highly likely that we can encounter today many contemporary documents that refer to Washington as the first president. (p. 97)

Or,

Given the hypothesis that Jesus was revealed through Jewish Scriptures, and background theories and information about the way Second Temple Jews used and adapted their Scriptures, it is highly likely that we can encounter many passages in the Jewish Scriptures that are alluded to in the Gospels and Epistles when talking about Jesus.

Or,

Given the hypothesis that education in Greek literacy required the study of Greek literature, and background theories and information about the way Second Temple Jews used and adapted Greek literature, it is highly likely that we can encounter at least some traces of Greek literary influences and ideas in the early Christian Greek literature.

Finally for now,

Pr(E|B) in words:

This is “the expectancy, the probability of the evidence given background information.”

For example,

If our evidence is an invitation to Washington’s inaugural, it is only to be expected, given all that we know. If, however, we find it in the archives of King George with a personal dedication from Washington saying, “hoping to see you there,” it is highly surprising and would require rewriting American historiography. (p. 97)

A early Christian studies example,

If our evidence is Christian apologetic writings that claim to quote a letter from Jesus to the king of Edessa, it can be dismissed as a fabrication given all we know. If, however, we found the letter in scientifically verifiable archives of King Abgar of Edessa, it would be very surprising and lead to a serious rethink about Jesus and Christian origins.

Pr(H|E & B) in words:

This is “the posterior probability of the hypothesis given new evidence and background information.” This is “the ratio of the likelihood of the evidence given the hypothesis and its prior probability, to the expectedness probability of the occurrence of the evidence whether or not the hypothesis is true.”

Let our hypothesis be that there was widespread literacy among speakers of the Y language in the time of X: . . . .

  • New evidence comes to light. It is a book in prose in the Y language and from the time of X.
  • Our background knowledge informs us that prose writings are associated with widespread literacy since the earliest (nascent) stages of literacy produce characteristically poetic (easily remembered) writings. Prose is a later development that accompanies growing literacy.
  • The posterior probability of our hypothesis that there was widespread literacy at this time among speakers of language Y is almost 1.

Or let our hypothesis be that Chinese printing caused the invention of European printing:

  • New evidence comes to light. It is a fourteenth century Persian text describing Chinese printing techniques.
  • Our background knowledge informs us that there are many possible scenarios where a Persian author might know about Chinese printing that do not require that knowledge to be transmitted to Europe.
  • Our posterior probability of our hypothesis that Chinese printing led to European printing is not increased by this new evidence.

Or imagine this (as per Tucker):

  • New evidence comes to light. It is Gutenberg’s diary in which he recounts meeting a Chinese merchant from whom he bought a Chinese printed book before the time of his printing press.
  • The likelihood of such evidence existing is very high given our hypothesis that Chinese printing led to the invention of printing in Europe. So the posterior probability of our hypothesis is dramatically increased by the discovery of the new evidence.

Discovery of new evidence does not necessarily mean tossing a stone into another cave and hearing the sound of it hitting a pot full of new manuscripts. Sometimes it can be an observation or record that has been in the literature but long overlooked.

I’ll cover more examples used by Tucker to demonstrate that Bayes’ theorem really does give us a symbolic representation of the processes by which historians really do evaluate hypotheses and test evidence.

Unfortunately, we will also see, by way of contrast, how theologians who think they are historians of the historical Jesus fail badly and really do not “do history like real historians do”. We will see that in fact many of them value what Tucker calls “therapeutic values” above “cognitive values”.

.

H/T Richard Carrier @ http://freethoughtblogs.com/carrier/archives/3923

.


*
Another critic of Carrier’s view, a theologian, has confused a Bayesian application to historical questions with classical logical-positivism. That, too, is a misinformed criticism: historians have long since (close to a hundred years now!) moved away from such positivism. Evidence is not theory-free. Theories are acknowledged today as necessary for deciding where to look for evidence, how we decide certain data is relevant evidence, etc. Clear thinking (which is all Bayes helps us to keep in mind) applies to more than just one philosophical approach to evidence and interpretation.

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33 thoughts on “Real Historians Do Bayes!”

    1. The beauty of your post is that it establishes a clear arguments with all factors and options given due consideration — which is the benefit of Bayes’ (the symbols are not necessary for this but are very useful! — and maybe it’s good to speak about it as symbolizing thought processes rather than as “maths”) — it is so easy to dismiss the virgin birth as “impossible” but of course this is sort of reaction always leaves room for protest. It makes all the factors transparent in arriving at a conclusion. (Not that a person of faith will be affected, but we are talking about “cognitive values” here, supposedly.)

    2. “The last one, Pr(E|H & B), looks like the likelihood instead of the posterior probability.”

      Damn, you’re right, of course. I repeated that one by switching my H and E around. It’s fixed now.

  1. My only problem with Bayesian probability is that the initial probability of anything is assumed and, therefore, arbitrary. This fact kind of renders Bayes’ Theorem a tautology that encourages a form of cognitive bias known as “anchoring and adjustment.” Garbage in is still garbage out. One of these days I will figure out how to demonstrate this formally in a Bayesian way.

    1. No, it’s not arbitrary. This is a common misconception. It’s merely a representation of what we believe the probability to be on the basis of current information. Take the letter of Jesus to the king of Edessa. How likely is it that that is a genuine letter? (I almost wrote “email” there!) If we think it is almost certainly genuine, then we can assign it a probability of anything, say, between 80% and 100%. That’s not an arbitrary range.

      We use these sorts of numbers all the time when discussing how much we like something or believe something to be true.

      Are we 50-50 on something? Or only slightly favouring one option over another, say 60-40? Do we think a horse has only a 5% chance of winning a race? We accept this number talk in everyday situations, and there is no reason to consider our numbers here any differently. In fact, that’s all we are doing in this case.

      What happens is that Bayes’ is helping us think carefully about each of our pieces of data and background information relating to it and to our hypothesis — so that we keep tabs on what bits are highly likely, what are highly unlikely, etc. to arrive at a balanced and well-considered decision at the end of it all.

      We don’t need Bayes’ theorem to do this. We can get exactly the same result without it. All Bayes’ is doing is assisting us to keep track of each piece of data that needs to be considered. All too often it is easy to overlook something or make a careless assumption along the way and then another scholar picks up our failing and the dialogue goes back and forth till we arrive at the “optimum decision”. By using Bayes we are encouraged to set all the details and assumptions out on the table and less likely to overlook or misjudge something in the first place. Bayes is simply a tool to help in the most efficient and best informed evaluations of evidence and hypotheses.

      1. “We don’t need Bayes’ theorem to do this. We can get exactly the same result without it”

        Yep.
        For decades I hung around lawyers and judges socially and professionally, cos of my job ,and even in social situations they loved to use words as qualifiers. It was a cultural habit.
        Take for example the statement above -“Take the letter of Jesus to the king of Edessa”. – my legal mates would have thrown in an ‘alleged’ thusly:

        “Take the alleged letter of Jesus to the king of Edessa”

        Bingo – the statement is no longer presented as one of given fact but as a questionable claim [‘claim’ being another qualifying word].
        Or:
        “In Mark 36.44″ Jesus says …” could be, should be presented as something like ” in the anonymous gospel ascribed to Mark, the author has his [or her] character Jesus say ….”
        Words like these plus ‘purported’, ‘supposed’, and probably several others should be far more widely used ,in the interest of accuracy and credibility , in Christian studies than they are .
        The result would be twofold [at least] – some incredibly clunky expressions as alleged and claimed and purported pile on top of each other but also a probably valid awareness that all too frequently we are reading claims not facts.

        1. This is the strongest benefit of Bayes’ — it forces inquirers to take note of exactly what it is that they are talking about. So often scholars will speak of the empty tomb as if it were raw data; in fact what is raw data is a narrative about an empty tomb. So the questions centre around the probabilities of this or that about the evidence we have — the narrative.

          If we don’t think we need to use it at all then it never hurts to do a check afterwards upon our own reasoning by setting it out and seeing how our results compare with a Bayesian conclusion. If it’s about the same, that’s reassurance. If it’s not, maybe we have been alerted to something we overlooked in our initial foray.

    2. Anchoring and adjustment only applies if you update once. BT is about updating multiple times, you don’t just use it once. And the driving force of BT are the conditional probabilities, not the prior. So as long as your conditionals aren’t arbitrary, two people who start out with vastly different priors can eventually converge as evidence is gathered. The only priors that aren’t useful are 0% or 100% since those aren’t probabilities

      So for example, if we have two people who are dealing with the Synoptic Problem — one starts with a prior of 90% that Mark was written first and the other starts with a prior of 22% that Mark was written first — it almost doesn’t matter where you start at because accumulating all of the evidence will push the two priors towards each other. And actually, if your prior is really in line with reality, then it won’t move much no matter how much evidence is gathered. So for example:

      Person 1 assumes the prior probability that Mark was written first, or P(Mark) = 90%. P(Mark) for the second person is 22%. The first evidence they analyze is the length of Mark. It is a fact that Mark is the shortest Synoptic Gospel (MSSG), so this is our evidence E (if Mark being the shortest gospel was only hypothetical, then the logic behind Occam’s Razor would apply, not BT). How likely is it that Mark would be the shortest gospel given that Mark was written first? A historian might look at this by doing a large survey of ancient works and see how many of the newer versions are shorter than the older versions. I’m not a historian so I wouldn’t know, but I would guess that the usual way it happens is that original compositions are shorter than the ones derived from them, though there could be shorter versions that came after the long version (like what’s argued is Marcion’s relation to Luke, at least until relatively recently). The word “usually” could be quantified in some way somewhere around 80% (since I don’t have the experience with historical documents that actual historians do). The third value we need is the false positive rate, or how many times a shorter document is actually a rewrite of a longer document. Again, not a historian, but this doesn’t seem like it happens a lot (5%). So for the sake of example BT would look like this:

      Person 1: P(Mark | MSSG) = P(MSSG | Mark) * P(Mark) / [P(MSSG | Mark) * P(Mark)] + [P(MSSG | Not Mark) * P(Not Mark)]
      : = .8 * .9 / [.8 * .9] + [.05 * .1]
      : = .9931

      Person 2: P(Mark | MSSG) = P(MSSG | Mark) * P(Mark) / [P(MSSG | Mark) * P(Mark)] + [P(MSSG | Not Mark) * P(Not Mark)]
      : = .8 * .22 / [.8 * .22] + [.05 * .78]
      : = .8186

      Both priors moved up, which makes sense since shorter documents are usually earlier versions of longer documents (but again, not a historian here).

      With our new priors, we look at some other evidence. Like the content only found in Mark such as Mk 8.22-26. How likely is it that this pericope would be in Mark given Mark’s priority? How likely is it that this pericope would be in Mark given some other Gospel’s priority, or restated, Mark added this pericope after reading the other Synoptics?

      Again, just for example since I’m not a historian, P(Mk 8.22-26 | Mark) is “probable” or 80% and P(Mk 8.22-26 | Not Mark) is “extremely improbable” or 1%.

      Person 1: P(Mark | Mk 8.22-26) = P(Mk 8.22-26 | Mark) * P(Mark) / [P(Mk 8.22-26 | Mark) * P(Mark)] + [P(Mk 8.22-26 | Not Mark) * P(Not Mark)]
      : = .8 * .9931 / [.8 * .9931] + [.01 * .0069]
      : = .9999

      Person 2: P(Mark | MSG) = P(MSG | Mark) * P(Mark) / [P(MSG | Mark) * P(Mark)] + [P(MSG | Not Mark) * P(Not Mark)]
      : = .8 * .8186 / [.8 * .8186] + [.01 * .1814]
      : = .9972

      As you can see, the two priors are starting to converge. And you would repeat the process for each piece of evidence both for and against Markan Priority, with the priors changed from the previous use of BT (i.e. the posteriors) functioning as the priors for the next line of evidence. Again, the driving force here is the conditional probabilities. Which makes sense since these two numbers are crucial for figuring out Bayes Factor, which determines how strongly the evidence either favors or disfavors your hypothesis.

      Of course in this example, my conditionals actually are subjective since I’m not a historian and would be a more invalid, subjective use of BT.

      1. @J. Quinton,

        Thanks for the response. I don’t think anchoring and adjustment is a one shot process, and I am not sure why you say it is. The anchor defines the range of acceptable possibilities and won’t disappear after one try. Indeed, one of the reasons mythicists are dismissed is because their views, regardless of how objectively reasonable they may appear, cannot be accepted. By comparison, even minimalists play by the same rules as maximalists and are worthy of criticism (as opposed to complete scorn). While you may be right that probabilities converge under BT, that is only true if you keep on applying it. Most people stop once they are satisfied.

      2. The major problem in your scenario is the establishment of a probability of the event in question. All of your choices in your calculation are arbitrary, and therefore one can easily go through a similar calculation using totally different probabilities, and show that the priors diverge. And then you have two opposite conclusions, and no method to determine which is closer to reality. This is what doctors often face when they give a test with false positive – you can end up with a person not having the disease and still have a 40% chance of testing positive. And in the doctor scenario, the probabilities are much more firmly established than in your scenario. I can only suspect that when it comes to religion and historical events, Bayes’ theorem is of little consequence.

        1. Hi Joseph — are you responding to J. Quinton above?

          If so, I don’t see how one can say that any assessments of probability are “arbitrary”. Surely not. Probability by definition even excludes arbitrariness.

          In Bayes calculations one has to iteratively justify one’s assessment of any particular probability. It’s not arbitrary. It’s justified or not by continual reference to more and more data.

    3. Bayes’ Theorem before anything else is a calculation. A calculation requires number, and those numbers are probability about real events such that any team of experts can verify those numbers. If I say 30% of college students in the US are non-believers, then this number can be verified by anyone. OTOH, saying that 30% of inhabitants of the Andromeda galaxy are atheists is unverifiable. The problem with certain claim such as the Jesus resurrection is that it is unverifiable. Putting a probability of its occurrence more likely than not will correlate with the bias of the person making that claim – an Atheist like myself will give it a probability of zero, while a Christian, 100% or very close to that. Using Bayes’ theorem (a calculation) will not settle anything as the probability that Jesus resurrected given the bible is true is not calculable.

      I understand the use Bayes spirit in evaluating a claim, historical, or otherwise, but unless you are doing a calculation, you are not using Bayes’ theorem. And people should stop making that claim.

      1. “Bayes’ Theorem before anything else is a calculation.”

        First, perhaps you need to adduce what evidence is valid and will alter the likelihood of H1/H2, given that “evidence” that is 50/50 likelihood on H1 and H2 is moot.

        In the end, no matter what historical argumentation you are modeling so as to evaluate the merits of, lack of knowledge either way must always come to a 50/50 likelihood and thus have no effect on the final probability of any theory. If some piece of evidence is just as expected to look that way no matter which theory turned out to be true, then it simply makes no difference to the probability of either theory. You can’t just “assume” one thing over another instead—that would be a straightforward fallacy of circular argument, which will be captured in the invalid likelihood ratio you would then be asserting. Likewise, all your probabilities must be conditioned on background knowledge. So, if all the documents you need to test a claim are lost, you cannot argue from what was or was not in them; because you don’t have them. Accordingly no “conspiracy theory” is needed to explain why something you expect is not reflected in the record—if there is no record, then you don’t know what it would have reflected had it survived. And this includes background knowledge’s effect on prior expectations. If a document looks like a piece of faked nonsense, then the probability it is must derive from the frequency of all other documents that look that way being that way. You cannot ignore the evidence of past cases; nor try to derive a preferred frequency from a false reference class (like claiming the Gospels look like rational-historical biographies, when they explicitly don’t).

        As such, Bayesian methods only quantify and thus describe, and therefore expose ordinary everyday reasoning about history, revealing when it is valid and sound, and when it is not. But to use it that way, you have to use it correctly. Just like any other method or logic.

        —Carrier (18 October 2021). “How to Correctly Employ Bayesian Probabilities to Describe Historical Reasoning (Jesus Edition)”. Richard Carrier Blogs.

        1. db, “You cannot ignore the evidence of past cases; nor try to derive a preferred frequency from a false reference class (like claiming the Gospels look like rational-historical biographies, when they explicitly don’t).”

          Well, that’s the crux of my argument. To an atheist like myself, the Gospels are false, but to a Christian like William Lane Craig, they are true. And when one has to decide the probabilities in such a situation, it is problematic.

          As an exercise, consider the following:

          EXERCISE 1
          What’s the probability that someone (like Jesus) can resurrect (=A), given the bible is true (=B)?

          Bayes’ Theorem says that P(A l B) = {P(B l A) X P(A)}/P(B)

          Step1
          We need to establish P(A), say what’s the probability of someone (like Jesus) resurrecting is true – that is, A = the event of someone resurrecting.

          What would you say about that probability? 10%, .01%, 0%, 50%. An atheist like myself would say 0%, or very near 0%. While a Christian like WLC would pick 10% or maybe even higher, 50%.

          See the problem?

          Step 2
          We need to establish P(B), say what’s the probability that the bible is true (=B) – Again, I would pick 0% or near 0%, while WLC would pick 100%, or very near that.

          Problem again with establishing a definite probability.

          Step 3
          We need to establish P(B l A ): what’s the probability of the bible being true, given someone can resurrect is true.
          Again, I would pick 0% or very near that, while WLC would pick 100%, or very near that.

          Step 4

          Let’s do the calculation P(A l B) according to Bayes Theorem: what’s the probability that someone like Jesus can resurrect (A), given the bible is true (B)?

          From the WLC’s point of view =100% x 50% / 100% = 50% (Step 1 = 50%)
          From the Atheist’s (mine) = 0% x 0% / 0% , which is undefined, meaning anything between 0 and infinity.

          What have we accomplished? Nothing, except that applying BT to events for which one cannot establish the probability as close to reality as possible is an exercise in futility.

          I think it’s important that we use BT in a situation we know it’s correct.

          EXERCISE 2

          What’s the probability of tossing a fair coin and getting two heads (H), given at least one coin is head (H)?

          BT says that P(A l B) = {P(B l A) X P(A)}/P(B)

          Event A = tossing 2 H
          Event B = tossing at least 1 H

          Step 1 There are 4 possibilities (HH, HT, TH, TT). Only one with 2 H: P(A) = 1/4
          Step 2 There are 3 possibilities (HH, HT, TH) with one at least 1 H out of 4. P(B) = 3/4
          Step 3 P(B l A) reads as the probability of tossing at least 1 H, given 2H. If given that you toss 2 H’s, you automatically have one H, P(B l A)=1.
          Step 4 P(A l B) = {1 X 1/4}/(3/4) = 1/3

          This is a valid calculation, as the probability of P(A), P(B) and P(B l A) are determined objectively, by which I mean, they can be verified independently by anyone. And that is not the case in EXERCISE 1.

          db, “If a document looks like a piece of faked nonsense, then the probability it is must derive from the frequency of all other documents that look that way being that way.”

          Again, this is a process that involves subjective decisions. Who determines that it is faked? Who determines which documents to be used in that process? The BT is based on the assumptions that one deals with real events in space and time, and that these events can be verified by any team of experts on the planet, and that one can objectively determines their probabilities. Many historical events, in particular those that have a religious slant, will inevitably fall off those requirements.

          1. “What’s the probability that someone (like Jesus) can resurrect (=A), given the bible is true (=B)?”

            Given Jesus b. Joseph/Pannera/etc. was an historical personage then:
            H1==JbJ did resurrect
            and
            H2==JbJ did NOT resurrect.

            Identify all known past global claims to an historical personage that did resurrect. Use these claims to create a prior for H1 and H2.

            If you get an H1 of zero historical personages actually resurrected per a thousand claims ..

            Then H1 is never ==0, and H2 is never ==1. They approach them but never equal them in Bayesian methodology.

            1. db:” If you get an H1 of zero historical personages actually resurrected per a thousand claims ..”

              What do we do with the claim of the resurrection of Lazarus in John (11:1–45)? Do we count that as evidence? And then we have Osiris and Baal in Ancient Egypt that are claims of resurrection, there are also many claims in Buddhism of the resurrection, in all of these claims, in order to do Bayes’ theorem, we need to establish a probability. How is that to be done?
              I reiterate: The BT is based on the assumptions that one deals with real events in space and time, that these events can be verified by any team of experts on the planet, and that one can objectively determines their probabilities of these events to occur.

              1. “The BT is based on the assumptions that one deals with real events in space and time, that these events can be verified by any team of experts on the planet…”

                “Well, that’s the crux of my argument. To an atheist like myself, the Gospels are false, but to a Christian like William Lane Craig, they are true. And when one has to decide the probabilities in such a situation, it is problematic.”

                db:” If you get an H1 of zero historical personages actually resurrected per a thousand claims ..”

                Question: What is Craig’s prior for “H1==JbJ did resurrect”?

                In other words, in the global “historical record” of claims that a historical personage did resurrect, how many did resurrect?

                What is Craig’s, yours, and mine. Mine is zero and I guess Craig’s prior approaches zero ..

                Arguably, establishing the prior for “H1==JbJ did resurrect” is an exercise in the “faith” of rational reasoning about the historical record 🙂

          2. Joseph, I think you have misunderstood the reason for Bayes and how it works. The beauty of Bayes is that people can start from totally opposing priors and by a process of iteration and step by step treatment of the evidence they will come to something close to the same result.

            So if one person says that the likelihood of Jesus being resurrected is 1% (or 0.1 or 0.00000000001% — it can never by 0 or a meaningful mathematical calculation cannot be done) and another begins by saying it is 99% (or 99.9999999% because it can never by 100% for the same reason) — then that is no problem at all. That is the sort of quandary that Bayes is designed to resolve.

            Bayes is used for search of sites where missing planes might have crashed. People can begin with very different starting points for a search: one the top north-east end of an area and the other the bottom south-west end of a possible area — Bayes calculations are revised each time someone tests the evidence for each site until one finds the actual site.

            Ditto with the question of Jesus’ resurrection.

            The problem would be that the apologist and the sceptic would have such divergent sets of assumptions, that as each bit of claimed evidence is introduced for discussion, it will lead inevitably to further Bayes assessments, and on and one, till one covers every quarter and that could end up many miles long. I think parties would have given up trying to get to the bottom of every one of each other’s assumptions before they get back to the question of the resurrection.

            But Bayes could certainly be a useful tool to resolve the question.

            What Carrier’s argument does is open debates on each of the data points of evidence that he has cited for a particular point related to the question.

            1. I will repeat my reply which I’ve already posted on one of Richard Carrier’s link:

              My objection is not with Bayes’ Theorem but with how it’s been used with respect to interpreting historical events that involve religious beliefs. We must keep in mind that the BT is based on the following assumptions: 1) that one deals with real events in space and time, in other words, these events can be verified by any team of experts on the planet; and 2) that one can objectively determine the probabilities of their outcome as precise as that can be carried out. Needless to say that any failure of these two assumptions would invalidate the use of Bayes’ Theorem.

              You might ask the question on how likely that the Jesus resurrection hinges on the probability of the body being stolen or reanimated, which to reasonable people it is a likely explanation. But to a Christian who believes that Jesus is the son of God, and as such, can resurrect. In other words, to that Christian the probability of Jesus resurrecting is 100%. You can see on that presumption what the BT would give as a result. Using the BT in debating with that Christian would get you nowhere. In fact, it might very well backfire on you. People like William Lane Craig are already doing that: using the BT to justify their beliefs. You might argue that they are applying the BT incorrectly. The point should be: you can’t use it. Period.

              1. Simply repeating your point without addressing my critique of it is not very useful. Bayes actually anticipates that some people will have differing prior as divergent as 99.9% and 0.1% — that’s the kind of difference Bayes works on and resolves.

                If anyone says a probability is 100% then they are not using Bayes at all – because 100% is absolute certainty and not even a probability. The answer will automatically be 100% just as it will be 0% is someone starts out at a 0% prior.

                The problem you are raising is not Bayes but the failure of one side in the argument to agree to use Bayes. — e.g. by claiming a 100% certainty (100% is a certainty, not a probability) they are not even using Bayes. The other problem you are raising, implicitly, is the refusal of one or both parties to actually go through the evidence together and to admit any possibility that any detail could go against them. Again, that has nothing to do with the validity of Bayes.

                But anyway, historians don’t use Bayes to decide if Jesus was resurrected. That’s a silly idea from the outset. It’s not even a historical question.

            2. Neil Godfrey: “Joseph, I think you have misunderstood the reason for Bayes and how it works.”

              Joseph Palazzo: It’s too bad you didn’t read my earlier post addressed to db, in which I illustrated with two exercises – 1) What’s the probability that someone (like Jesus) can resurrect (=A), given the bible is true (=B)? And 2) What’s the probability of tossing a fair coin and getting two heads (H), given at least one coin is head (H)?

              I showed step by step how to use the BT and calculate the probabilities in order to answer each of those questions. I deliberately use these two situations – one a “historical” religious event, the other, a “real” event to make the point that Bayes’ Theorem applies to one (exercise 2) and is problematic in the other case (exercise 1). I strongly suggest you read that post if you want to understand what I’m trying to say.

              Now I’m not sure of your position. In one post, you wrote:

              Neil Godfrey: “Ditto with the question of Jesus’ resurrection.

              The problem would be that the apologist and the sceptic would have such divergent sets of assumptions, that as each bit of claimed evidence is introduced for discussion, it will lead inevitably to further Bayes assessments, and on and one, till one covers every quarter and that could end up many miles long. I think parties would have given up trying to get to the bottom of every one of each other’s assumptions before they get back to the question of the resurrection.

              But Bayes could certainly be a useful tool to resolve the question.”

              And in a second post, you wrote

              Neil Godfrey: ”But anyway, historians don’t use Bayes to decide if Jesus was resurrected. That’s a silly idea from the outset. It’s not even a historical question.”

              Joseph Palazzo: My concern is about what some people are doing with the BT in such cases as deciding if Jesus resurrected. It’s the main reason why I’m posting here. I wrote in another post: “People like William Lane Craig are already doing that: using the BT to justify their beliefs. You might argue that they are applying the BT incorrectly. The point should be: you can’t use it. Period.”

              1. Joseph, it was what I read in your comment that I directly responded to. You said I should have read your two exercises. In exercise 1 you wrote:

                What would you say about that probability? 10%, .01%, 0%, 50%. An atheist like myself would say 0%, or very near 0%. While a Christian like WLC would pick 10% or maybe even higher, 50%.

                See the problem?

                It was that very statement of yours that I was responding to, pointing out that it was not a problem at all, that Bayes is designed to “work” no matter whether a person starts at 99% probability or 1% probability – the same result will ensue if both parties apply all iterations to the same steps that follow.

                I also pointed out that 0% and 100% are not probabilities so by using those figures you are not using Bayes at all. They are absolute certainties, not probabilities, and allow for no further discussion.

                Bayes is not the problem. The only problem is whether people agree to use it or not on all the available evidence. Usually one side at least will spit the dummy when they see a shift in probabilities they do not like.

  2. Thanks, J. Quinton. A much more competent response than my amateurish effort.

    Just for interest, here are a few extracts from the “preface and note to readers” in The theory that would not die : how Bayes’ rule cracked the enigma code, hunted down Russian submarines, & emerged triumphant from two centuries of controversy by Sharon Bertsch McGrayne:

    On its face Bayes’ rule is a simple, one-line theorem: by updating our initial belief about something with objective new information, we get a new and improved belief. To its adherents, this is an elegant statement about learning from experience. Generations of converts remember experiencing an almost religious epiphany as they fell under the spell of its inner logic. Opponents, meanwhile, regarded Bayes’ rule as subjectivity run amok. . . .

    At its heart, Bayes runs counter to the deeply held conviction that modern science requires objectivity and precision. Bayes is a measure of belief. And it says that we can learn even from missing and inadequate data, from approximations, and from ignorance. . . .

    It has become a metaphor for how our brains learn and function. . . .

    1. Neil Godfrey: “Bayes is designed to “work” no matter whether a person starts at 99% probability or 1% probability – the same result will ensue if both parties apply all iterations to the same steps that follow.”

      You’re missing the point: It’s my long experience that Atheists and Christians don’t agree on what constitute evidence. Applying BT on the Jesus Resurrection, or the Virgin birth, is an exercise in futility. But the danger is that people like Richard Carrier inadvertently have open the door to people like William Lane Craig on the use of the BT for their own purposes. Unfortunately I don’t seem to make headway with Atheists as they think they have the nukes to destroy people like WLC. They don’t. Anyway, this discussion is over.

    1. Even religious claims and false propaganda use logic and reason. 🙂

      And I’ve posted here on scientific methods in historical analysis, most recently with respect to “scientific methods of dating” texts.

      But I invite you to read, say, my earlier posts on Carrier and how Bayes sits against the nature of historiography as understood by most historians themselves. Even Tucker Tucker calls “historiography” a science, but why not take up my suggestion from some months ago and actually read what historians themselves believe they are doing? One well known book to start with is On “What Is History” by Jenkins. It won’t hurt, unless readjusting long held preconceptions really hurts. You might actually expand your understanding.

      1. Even religious claims and false propaganda use logic and reason.

        True, but they also use ill-logical and un-reason. History (if you want to do it well) should not. [In saying that I am presuming, of course, that there is historical truth, however imperfectly humans can attain it, and that it is not merely an arbitrary social construction. But then I presume that you are committed to that position also?]

        1. I do wish you would read what historians themselves explain about the nature of their work. None so blind as he who will not see. “Historical truth” is a highly debated construct among historians. If you mean simply an historical fact, such as that Julius Caesar crossed the Rubicon, and call that “historical truth”, then that’s fine if by “truth” you simply mean an existing “fact”. But historians do a lot more than merely record chronicles nowadays.

          1. I do wish you would read what historians themselves explain about the nature of their work.

            As I’ve replied several times, I have read what they say and I am aware of what they say.

            None so blind as he who will not see.

            On this issue you seem very like a Jesus-historicist, simply pointing to a mainstream consensus as though that settles it and refusing to discuss the issue further. You of all people should realise that just because a group of people have agreed something among themselves doesn’t make it right.

            “Historical truth” is a highly debated construct among historians.

            Indeed so, and opinions range all the way from those who argue the postmodernist stance that there is no “truth” and that the different accounts are merely social constructions, to those who consider that there is indeed a truth about historical events, at which they are trying to get. I’d consider that the “real” historians, who use Bayes and evidence, are in the latter camp.

  3. Some recent attempts on alt argumentation for Yesus:

    Someone recently produced an argument more or less like this: there’s a 75% chance the Gospels contain some historically true facts about Jesus, and a 75% chance Paul is talking about biology when he mentions Brothers of the Lord, and a 60% chance the Jewish execution of Jesus in 1 Thessalonians 2 has not been interpolated, and a 60% chance Josephus recorded something true about Jesus, and a 50% chance Papias knew actual eyewitnesses to a historical Jesus, therefore Jesus more likely existed.

    —Carrier (12 December 2022). “The Jesus Chronicles: Three Things People Get Wrong about Probability”. Richard Carrier Blogs.

    “Does Mythicism Have To Be 100% Correct? feat. Kamil Gregor”. YouTube. Godless Engineer.

    1. Oi, you said the conversation was over yet here you are — continuing to avoid addressing my explicit criticism of the point you said I failed to read. Your paper is wide off the mark as regards the discussion of evidence, though. The evidence is not “Jesus walked through walls”, for example, but that “a gospel narrative describes Jesus as walking through walls”. Your paper misses the very nature of evidence.

      Both parties can agree that the gospel makes a claim for a miracle. The discussion begins at that point. Otherwise no-one is using Bayes so it is pointless to find fault with Bayes in such a situation.

      (A ghost sighting is not evidence. What is evidence is that so-and-so says they saw a ghost.)

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